Gabriel opened a bank account. The balance is adjusted at a constant rate each week. This equation y = 15x + 35 can be used to represent this situation, where y is the account balance in dollars and x is the number of weeks since he opened the account.

Which statement best describes the account balance, given this equation?

Gabriel opened the account with $35 and is deducting $15 per week from his bank account.

Gabriel opened the account with $15 and is depositing $35 per week into his bank account.

Gabriel opened the account with $15 and is deducting $35 per week from his bank account.

Gabriel opened the account with $35 and is depositing $15 per week into his bank account.

80

step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt